A041241 Denominators of continued fraction convergents to sqrt(132).

1, 2, 45, 92, 2069, 4230, 95129, 194488, 4373865, 8942218, 201102661, 411147540, 9246348541, 18903844622, 425130930225, 869165705072, 19546776441809, 39962718588690, 898726585392989, 1837415889374668, 41321876151635685, 84481168192646038

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,46,0,-1).

Crossrefs

Cf. A041240, A040120, A042011.

Programs

Magma

I:=[1, 2, 45, 92]; [n le 4 select I[n] else 46*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

Mathematica

Denominator[Convergents[Sqrt[132], 30]]  (* Vincenzo Librandi, Dec 13 2013 *)
LinearRecurrence[{0,46,0,-1},{1,2,45,92},30] (* Harvey P. Dale, Jun 15 2022 *)

Formula

G.f.: -(x^2-2*x-1) / (x^4-46*x^2+1). - Colin Barker, Nov 14 2013

a(n) = 46*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 13 2013

a(2*n) = A042011(2*n) = numerator of continued fraction [4,11,4,11,...,4,11] with n pairs of 4,11. - Greg Dresden, Aug 10 2021

Extensions

More terms from Colin Barker, Nov 14 2013